Question: Rewrite as a simplified fraction. ${0.\overline{83} = {?}}$
Let $x$ equal the decimal. Set up two equations such that the digits after the decimal point are identical. ${\begin{align*}100x &= 83.8383...\\ 1x &= 0.8383...\end{align*}}$ Subtracting the two equations, we have: ${99x = 83}$ ${x = \dfrac{83}{99}} $